Except the book cover DOESN'T parody their product. It uses elements of their well-known trademark to promote the author's product. That's what gives JD grounds to take action. Not that they needed a make-able case to file suit anyway, if they wanted to go that route.
Which makes the fact that JD chose to try to resolve it nicely even more impressive. Now the Streisand Effect is working in their favor.
EDIT: In your example, the Daily Show is using and parodying Fox's material and logos in order to comment upon and criticize Fox. That is indeed Fair Use. The Jack Daniels book cover isn't as cut-and-dried a case, it might well take a court to resolve it. Again, damn good move by JD to play nice, assume no infringement was deliberately intended, and handle it the way they did.
Now, if the author had responded with "Nyah nyah, fair use, can't touch me muthafarkers, eat me!" the next correspondence would have been a bit less pleasant.